5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Squares, first question
This topic has expert replies
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Nobody answered this? Come on, guys 
x² + 1/x² = 4
(x² + 1/x²)² = 4² = 16
but we also know that (x² + 1/x²)² = x� + 2 + 1/x�
so x� + 2 + 1/x� = 16, and x� + 1/x� = 14
x² + 1/x² = 4
(x² + 1/x²)² = 4² = 16
but we also know that (x² + 1/x²)² = x� + 2 + 1/x�
so x� + 2 + 1/x� = 16, and x� + 1/x� = 14
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
IMPORTANT: I notice that if we SQUARE x², we get x�, and if we SQUARE 1/x², we get 1/x�, so let's see what happens if we take the equation x² + 1/x² = 4 and SQUARE both sides:If x² + 1/x² = 4, then x� + 1/x� = ?
A. 10
B. 11
C. 12
D. 14
E. 15
(x² + 1/x²)² = 4²
So, (x² + 1/x²)(x² + 1/x²) = 16
Expand to get: x� + 1 + 1 + 1/x� = 16
Simplify: x� + 1/x� = 14
Answer: D
Related Video:
Using the FOIL method to expand expressions: https://www.gmatprepnow.com/module/gmat ... /video/952
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
In addition to my algebraic method above, you can also always try to gut out an approximation. (This isn't ideal here, since the answers are packed tightly together, but it's a fallback plan on test day.)
If x² + 1/x² = 4, then we know x should be slightly less than 2. (2² + 1/2² = 4.25, which is close).
By that logic, our answer should be slightly less than 2� + 1/(2�). From there, we should have D or E (... and it's a coin flip).
If x² + 1/x² = 4, then we know x should be slightly less than 2. (2² + 1/2² = 4.25, which is close).
By that logic, our answer should be slightly less than 2� + 1/(2�). From there, we should have D or E (... and it's a coin flip).
